The Republican Party’s presidential frontrunner Donald Trump has repeated his claim he did not have anything to do with a National Enquirer story that suggests his rival, Ted Cruz, had five affairs.

But he did float the idea that there was something seedy in Mr Cruz’s wife’s past, which could spark a new feud between the two.

“I had nothing to do with it, the campaign had nothing to do with it,” Trump told ABC.

Refusing to condemn it, Mr Trump said: “I don’t care, I don’t care, the National Enquirer did a story, it was their story, it wasn’t my story, it was about Ted Cruz, I have no idea if it was right or not.

“They actually have a very good record of being right. But I have absolutely no idea.”

Turning to Mr Cruz’s wife, Heidi, Mr Trump said: “Well, there are things about Heidi that I don’t want to talk about, but I’m not going to talk about them. You can look, but I wouldn’t talk about them. Frankly, I hope it’s not right.”

The row over the National Enquirer story capped ab already nasty week in politics between Mr Cruz and Mr Trump.

It began with an ad that came out – courtesy of the Make America Awesome super PAC – that showed a nude Melania Trump in an attempt to “slut shame” the potential first lady and have voters choose Mr Cruz instead.

Mr Trump suggested that Mr Cruz’s fingerprints were all over that ad and maintained that position at the weekend. “And just so you understand, that super PAC is very friendly to Ted Cruz, he knew all about it, 100 per cent, so he started it, I didn’t start it,” he said.

Mr Trump alleged that it was the Cruz campaign which bought the rights to the nude photo, part of GQ photoshoot, which Mr Trump described as “a very strong modeling picture, no big deal”.

“He’s very close to the super PAC, just so you understand that,” Mr Trump. “And there’s no way in a million years that that super PAC did that without his knowledge.”

Lyin’ Ted Cruz is now trying to convince prople that his problems with The National Enq.were caused by me. I had NOTHING to do with story!

“Don’t forget I call him ‘lyin’ Ted’, I call him that because nobody that I’ve known – I’ve known a lot tougher people over the years in business – but I’ve never known anybody that lied like Ted Cruz.”

Mr Cruz has repeatedly denied that his campaign had anything to do with the initial attack on Melania Trump.

“Not remotely, it was a group, I do not know the person who was involved,’ Cruz said. ‘As far as I know, I’ve never met them, I’ve never spoken to them. They’re completely disconnected from our campaign. The ad they put out was deplorable,” he told Fox News.

“And as soon as I saw it I denounced it and said it was wrong, but it wasn’t us.”

At the time, Mr Cruz put out an olive branch of sorts on Twitter, writing: “Donald, real men don’t attack women. your wife is lovely, and Heidi is the love of my life.”